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Sliding of glacial ice over its base is typically described by a frictionless or slowly deforming bed. This view is challenged by recent seismic observations of stick-slip motion at the icebed interface. We revisit a high-frequency (20–35 Hz) harmonic tremor recorded on Gornergletscher, Switzerland. In contrast to previous interpretation in terms of glaciohydraulic tremor, we present evidence for superimposed stick-slip episodes as tremor sources: we locate the tremor source with matched field processing polarity optimization, which allows for azimuthal polarity patterns associated with nonisotropic moment tensors and yields a tremor source clustering near the glacier bed. Our analysis confirms an S wave radiation pattern in agreement with a double-couple source derived from ice sliding over bedrock and explains our tremor observations in terms of glacier stick-slip motion. Adding to observations of stick-slip tremor beneath polar ice streams, this first report on stick-slip tremor beneath Alpine ice favors widespread seismogenic glacier sliding.